WOMEN AND MINORITIES IN SCIENCE

Prospects for women and minority doctoral scientists
in engineering and other math-intensive areas are examined. A calculation
of the ethnic-gender profile of this segment of the workforce is made for
U.S. citizens and permanent residents. Rank ordering on mathematical reasoning
ability predicts that women will top off at approximately 27 percent of
this market. Similarly, rank ordering predicts almost 99 percent of math-intensive
doctoral jobs will go to whites and Asians of primarily Chinese, Japanese,
Korean and South Asian descent. Asians will continue to be represented in these fields
well beyond their numbers in the general population. A study of the math-intensive
academic marketplace predicts that women will top off there at about 22
to 23 percent.

WOMENRecruitment of women into science and engineering is a national mission.
Equal pay for equal work is part of the story, but the principal goal is
numerical equality for women, especially in fields where they have not
fared well. Colleges, universities, government and industry are joined
in the battle. Government and industry provide the money, universities
the training. It is a team effort.

From the University of Texas we read:

"Diversity derived from inclusion of all groups is essential
for solving the engineering challenges of the 21st Century. Women are a
vital human resource for this endeavor. The Women in Engineering Program
is an agent for intervention and a catalyst for transformation."

From Rensselaer an invitation is extended:

"A scholarship fund endowed by your corporation would be
a major help in attracting women to Rensselaer. A scholarship of $5,000
per year for four years would allow your company to sponsor a Rensselaer
scholarship named after your corporation."

At Georgia Tech a University task force reports the following:

"As part of a leading education and research institution
in the nation, the College of Engineering at Georgia Tech will provide
an environment conducive for women to pursue successfully and in a professional
manner an engineering education and career."

Seems harmless enough but let's look at how Georgia Tech increases enrollment
of women engineers. It uses a favorite trick of the gender-equity crowd.
They manipulate entrance requirements. In 1992, the Engineering School
at Georgia Tech weighted the math SAT score 9.5 times greater than the
verbal SAT score in the admissions formula. These relative weights were
assigned on the basis of a grade-predicting regression analysis. Two years
later in 1994, the admission index weighted the math score on the SAT only
3.8 times as much as the verbal score. Four years later in 1998, application
essays and leadership ability were included in the admissions formula.
Because women scored significantly lower than men on the math SAT, Georgia
Tech manipulated admissions criteria to de-emphasize mathematical ability,
and included new subjective criteria. Between 1994 and 1997 Georgia Tech
established a double standard for admissions. In this period entering female
students averaged 29 points (about 0.3 standard deviation) lower than their
male counterparts on the math SAT. The same game is played at hundreds
of colleges and universities across the country.

Graduate schools are also swept up in the gender-equity game. A movement
to increase graduate degrees among women in engineering and science is
vigorous and widespread. These efforts have substantially narrowed the
numerical gap between men and women new PhDs. Women currently account for
more than 45 percent of new PhDs in the biological sciences. Attempts in
the more mathematically based disciplines have been less successful.

We isolate four technical fields that lean heavily on mathematical aptitude:
engineering, physical science, computer science and mathematics. These
disciplines span the math-intensive areas. The gender gap there is more
resistant to closure. How much narrowing can we expect? Will women ever
be proportionally represented in these technical fields? Will encouragement,
financial incentives and admissions chicanery be enough to eliminate the
gap? We will address these issues here.

Evidence points to a gap between men and women in mathematical reasoning
ability. Men seem to have the edge. Though statistical in nature, the gap
is sufficiently large that most people suspect it simply from their life
experience. Evidence, however, raises the issue above the level of suspicion.
Simply put: On all standardized exams, including IQ tests, men score
higher than women on mathematical reasoning sections. The effect crosses
all races and cultures. It may be biological or environmental in origin,
but that is another issue. We merely note that all efforts to erase the
math gender gap have failed.

In a bias-free employment market it is possible to calculate the maximum
proportion of women that we can expect to be employed at the doctoral level
in the collective areas of engineering, physical science, computer science
and mathematics. We will gauge the efforts of government, industry and
universities against the results of this calculation.

DEFINING THE GAPThe math gap is ubiquitous, and can be assessed from as simple an instrument
as the Scholastic Assessment Test (SAT). For many years boys have outperformed
girls on the mathematical reasoning part of this exam. After small gains
by women, the difference in performance leveled out and has remained remarkably
constant for years. The gap persists, not withstanding that girls get better
grades in school and despite considerable efforts to bring the male and
female averages together. Figure 1 shows eleven years of Math SAT averages
for men and women. Both sexes show a general upward trend from 1984 through
1994, but the male - female difference has remained almost constant.

In 1998, more than a million college-bound high school seniors took
the SAT I mathematical reasoning test, 541,962 men and 630,817 women. Men
averaged 529.6 (SD = 114.1). Women averaged 494.5 (SD = 107.8). Since the
two distributions have slightly different standard deviations, we computed
the gap as the difference in the means divided by the root mean square
of the two SDs, obtaining a male-female math gap of 0.32 SD.

Math SAT scores range between 200 and 800. (You get 200 for writing
your name.) Contrary to popular belief, 800 is not a "perfect score." It
simply means that some threshold has been reached. Two students, each with
scores of 800, will not necessarily have done equally well. A few years
ago the College Board changed its scoring system. They called it "recentering."
Ostensibly, recentering was designed to bring both the verbal and mathematical
averages closer to 500. There were, however, other only rarely mentioned
consequences. Recentering compresses the distribution of scores near the
top, so that the best students become difficult to distinguish from
one another. The new scoring system blurs the line between excellent and
exceptional. Truly special students get lost in the crowd of very good
students. In the year just before the SAT was recentered, 32 students nationwide
scored a "perfect" 1600 on the combined math and verbal exams. The following
year, after recentering, 545 students scored 1600, about 17 times more
than under the old system. Coincidence or not, recentering is part of a
leveling process in education, which attempts to minimize differences between
students. With recentering, high scorers cluster together near the top
of the distribution, making it easier for very selective schools to justify
admitting more minorities. The SAT no longer distinguishes high-scoring
minorities from higher achieving Whites and Asians. Nonetheless, despite
all these limitations the SAT remains an extraordinary tool.

Only about 30 percent of youngsters who are high school senior age take
the exams. They are not representative of American youth. More girls than
boys take the exams. Some students headed for college take the American
College Testing Program (ACT) exams rather than SATs. Others who do not
take SATs have taken themselves out of the college marketplace. Some have
dropped out of school. For all these reasons SAT takers are not representative
of their age group, and plausibly we might be criticized for using
SAT results to assess a general gender difference. Addressing this problem,
we can infer from a few mild assumptions the distributions of SAT scores
that would be obtained if every person in the country of high school
senior age took the exam.

Most of the brightest students take SATs, even those from ACT states.
A senior in an ACT state who is even thinking of applying out of state,
will take SATs. Thus, we can assume with little error that just about all
the brightest youngsters in the age group will take SAT exams. They will
place in the high-end tail of the distribution. Consequently, the high
end region of the curve will look more-or-less as it would if every last
person in the age group took the exam. From the characteristics of the
high-end tail we can reconstruct the full distribution as it would look
for the entire high school senior age population.

Let PM(x)dx be the probability of a
male obtaining an SAT score between x and x + dx.
Let PF(x)dx be the corresponding probability
for a female. (The quantity, x, is in SD units.) Now suppose that
each of the two distributions is Gaussian, with equal standard deviations.
Further, the distributions are displaced from one another by a gap, Δ,
such that:

(1)

The quantity, Δ, is the difference between
the mean scores, male - female.

Let fM and fF be the fractions of
males and females who obtain the score, l, or
better. Then,

(2)

and

(3)

For convenience, we note the following transformation:

(4)

and write for fF,

(5)

In 1998, 0.765 percent of the entire resident population of male
17-year-olds in the U.S. took the SAT math exam and scored 750 or higher,
compared with 0.318 percent of the corresponding females. That is, fM
= 0.00765 and fF = 0.00318 for λ
(in SD units) equivalent to a 750 SAT score. Further along the tail,
0.430 percent of the resident men in this age group scored 780 or better,
compared with 0.164 percent of the corresponding women, i.e., fM
= 0.00430 and fF = 0.00164 for λ
equivalent to a 780 SAT score. We can be confident that both rarefied groups
contain just about all of the nation's most mathematically talented 17-year-olds.

From these data we can obtain the difference between male and female
means for the entire age group. Assuming a normalized Gaussian probability
density centered on zero, (2) may be solved numerically for λ,
the number of standard deviations the threshold score is displaced from
the mean score of PM. For a score of 750, we find λ
= 2.43; for a score of 780, λ = 2.63. Knowing
λ, (5) may be solved numerically for Δ,
the gap between the male and female means. The 750 cutoff yields Δ
= 0.303, and the 780 cutoff returns the value Δ
= 0.313. Both results are remarkably close to the gap of 0.32 SD observed
from the group of just test takers. We will use the value, Δ
= 0.31 SD.

According to the 1995 Survey of Doctorate Recipients published
by the National Science Foundation, that year 181,800 doctoral scientists
were employed as mathematicians, computer scientists, physical scientists
and engineers. In 1995, women made up 9.7 percent of this workforce. If
the 181,800 slots were filled strictly according to mathematical aptitude,
a different proportion would have emerged. We solve a rank order problem
to find that proportion.

Suppose NS slots are to be filled in order of ability
from a pool of NM men and NF women.
Assuming a distribution of ability, all those with ability equal to or
greater than some value, λ, will be selected
to fill a slot. The cutoff ability, λ, can be
determined from the pool sizes, the number of slots available and the ability
distributions for men and women. The variables are related as follows:

(6)

The first term on the left side of (6) represents the number of males
who make the cutoff; the second term is the corresponding number of females.
The two terms add up to the number of slots, NS. From
the pool sizes, NM and NF, the number
of available slots, NS, and the gap between the male
and female distributions, Δ, we may find the
cutoff ability, λ, by solving (6) numerically.
Knowledge of λ allows evaluation of the first
and second terms on the left side of (6) giving the number of men and women,
respectively, selected to fill the slots.

For NS = 181,800, the number of doctoral scientists
employed in math-intensive areas in 1995, we calculated the expected percentage
of females, assuming the slots would be filled in rank order of mathematical
ability. The calculation proved not very sensitive to pool sizes so long
as the ratio of men to women remained essentially constant. We formed the
pools from men and women between the ages of 25 and 65, using 1996 population
data. In this age range there were 68.7 million men and 70.8 million women
resident in the U.S. in 1996. The quantities, NM and
NF, were set to these values, respectively. The resulting
calculation predicted that female doctoral scientists will saturate the
math-intensive marketplace at approximately 27 percent.

ConclusionsThe 1995 figure of 9.7 percent women doctoral scientists in math-intensive
fields leaves lots of room for increased participation before the predicted
limit kicks in. Many of these women entered the workforce years ago, before
the drive to get women into the sciences, so we should look for an increasing
female presence over the next few years. Across the fields of engineering,
mathematics, and physical and computer sciences, there is wide variation
in the representation at the doctoral level by women. In 1995 for example,
at the doctoral level women made up 11.7 percent of physical scientists,
10.6 percent of computer scientists, 4.9 percent of engineers and 17.7
percent of mathematicians. Overall, 9.7 percent of the doctoral scientists
in these areas were women. Thirty years ago, women were so poorly represented
in the highest levels of the technical workforce, that they were all but
invisible. Since then, they have made enormous gains, but are still underrepresented,
especially in engineering. They have come a long way, but will soon run
into a statistical barrier, penetrable only by political or social intervention.
Looking at recent doctoral recipients, we get a sense of the workforce
of the future. In the combined areas of physical science, mathematics,
computer science, and engineering, women earn more PhDs than before. In
1983 only 10 percent of these degrees went to women. By 1988, the proportion
was up to 14 percent. More recently, the 1995, 1996 and 1997 numbers were
up to 20.5, 19.3 and 19.8, respectively. Room for further increases still
remains before the ladies bump up against a statistical ceiling near 27
percent.

SUPER ELITE WOMENAmong doctoral scientists, a more elite segment may be found. They
are the faculty of research universities. An academic department in a research
university is like a ball club. Faculty members push the envelopes of their
research to enhance their reputations, but they also like to be on a winning
team. Building the department's reputation is important. The department's
appetite for talent is insatiable. When a position opens, a search is launched
worldwide to attract the best person. The academic marketplace is matched
only for dog-eat-dog aggressiveness by major league sports.

When finally appointed, a new junior faculty member must hit the ground
running. He has a six year contract, but in reality he has only four and
a half years to prove himself. A tenure decision will be made in the middle
of his fifth year. It is the most critical time of his life. He has been
preparing for this moment since he was an undergraduate. After the B.S.,
four or more years in graduate school, at least two years of postdoctoral
training in another laboratory, and he is ready to fly on his own. Four
and a half years later he will come up for promotion and tenure. It is
up or out. Failure to get tenure means he must leave the university. If
he fails, he will have the remaining year and a half of his contract to
find a new job. Though publicly denied, in practice the candidate will
be judged solely on the research criterion. It is a fair system because
both the candidate and the department understand the rules from the outset.

In the short time the candidate has been at the university, he is expected
to have attracted independent funding, to have produced significant research
output, and have established a national reputation in his field. A committee
of peer plus department members and at least one outsider will decide his
fate. Often students are included to help with the evaluation of teaching.
However unless the candidate is a basket case in the classroom, he will
satisfy the teaching criterion. The evaluation turns primarily on the assessment
of outside referees, the most renowned investigators in the candidate's
field. Each is asked to evaluate the candidate's work, with which they
should already be familiar. The fundamental question is whether this candidate,
in the past four plus years has done the quality work expected in academic
research. If the answer is yes, the candidate will be advanced to tenure
and promotion. Characteristically, about half the candidates make it. The
elite group of academic scientists who obtain tenure represents the cream
of American science. We ask at which point this market will saturate
with women?

To obtain the number of available slots in our rank order game, we must
count the tenured faculty who work in math-intensive disciplines in American
research universities. We can make a ballpark estimate of their number
by looking at a product of their labors: new PhDs. For the last few years
our universities have been turning out twelve to thirteen thousand PhD
scientists a year in the math-intensive fields. Most are produced by senior
faculty. Assuming an average of one new PhD per year per tenured faculty
member, we estimate the number of slots to be 12,000 or so. The calculation
proves only mildly sensitive to slot size, making the ballpark estimate
sufficient.

In the math-intensive areas, what is the fraction of tenured research-university
faculty that we can reasonably expect to be female? Equation (6) again
provides the answer. For a gap, Δ = 0.31, slot
sizes, NS, between 8,000 and 17,000 (bracketing our ballpark
estimate) and pool sizes, NM and NF,
taken as the populations in the 25 to 65 age bracket, we predict that women
will saturate this academic market at between 22 and 23 percent. With fewer
slots available, women do not fare quite as well. Table 1 summarizes the
results.

pool of men
NM (million)

pool of women
NF (million)

number of slots
NS

predicted percentage
of women

68.7

70.8

8,000

22.3

68.7

70.8

17,000

23.3

Table 1. Predicted percentage of women that will saturate
the market of tenured faculty at research institutions in the specified
math-intensive disciplines.

MINORITIESThe College Board groups SAT takers into several ethnic categories.
The groups include American Indian or Alaskan Native; Asian, Asian American
or Pacific Islander; African American or Black; Mexican or Mexican American;
Puerto Rican; other Hispanic and White. The Asian/Pacific Islander designation
is particularly troublesome because the facts suggest that within this
category are very disparate groups including the very bright and the very
dull. In fact, the 1990 census shows that the Asian/Pacific Islander category
for SAT purposes includes Chinese, Filipino, Japanese, Asian Indians, Koreans,
Vietnamese, Cambodians, Hmong, Laotian, Thai and other Asians. Also included
are Pacific Islanders, which further subdivide into Polynesian Hawaiians,
Samoans, Tongans, other Polynesians, Micronesians, Guamanians, Melanesians
and unspecified others. Out of these, 48 percent are Chinese, Japanese
or Korean, the troika of high achievers.

All the groups designated by the College Board have math SAT distributions
with standard deviations clustered about 100, except the Asians/Pacific
Islanders. And no wonder. Their standard deviation is closer to 120, showing
their diverse nature. The distributions for 1987 for both Asians and Whites
are shown in Figure 2, where the qualitative difference between the two
distributions is apparent to the naked eye. The distribution for Asians
is uncharacteristically broad, with a flattened top. It hints at bimodality.

An attempt was made to fit the "Asian" MSAT distribution for 1987 and
1992 (the years for which we had access to the ethnic distribution data)
to a sum of Gaussians. Since the elite Chinese, Japanese, Koreans and South Asians made
up about half this group, the Gaussians were given equal weight. (See Figure
3.) The least-squares fit suggests that this Asian quartet performed with
a mean of approximately 627 for 1987 and 641 for 1992. The remaining Asians
had mean scores of approximately 426 (1987) and 444 (1992), not unlike
American Indians. Choosing Whites as the reference group (Δ
= 0), and averaging over both years yielded Δ
= -1.24 for elite Asians, and 0.47 for other Asians. Other group Δ's
were obtained from 1998 MSAT mean scores as follows: Hispanic = 0.683,
Black = 0.99, and American Indian = 0.437. A rank order analysis, similar
to that used for the sexes, was performed using an extension of (6):

(7)

where PW is the normalized distribution function
for Whites, Ni is the number in the pool from the ith
group, and the sum is over all groups.

The number of slots, NS, was set equal to 181,800,
the number of doctoral scientists employed in 1995 in the selected technical
fields. Again, we used the 25 to 65 age range for the pool numbers, this
time for each racial or ethnic group. We allowed for multi-talented people
to choose completely different fields by cutting the pool sizes for each
group proportionately and incrementally from the full populations down
to 1/5 of the full pool. The resulting predictions thus fall into ranges.
They are summarized in Table 2. For comparison, we also show
the percentage of doctorates actually awarded to U.S. citizens and permanent
residents in the selected fields in 1995.

Table 2. Predicted percentages, by race and ethnicity,
of jobs filled by doctoral scientists in math-intensive fields if filled
in rank order of mathematical ability. Also shown, for comparison, are
percentages of doctorates awarded in these fields in 1995 to U.S. citizens
and permanent residents.

ConclusionsLa Griffe predicts that the PhD market in the math-intensive
technical areas will saturate at almost 99 percent White and Asian. Of
the Asians, almost all will be either Chinese, Japanese, Korean or South Asian. Whites
will fill 59 to 72 percent of the jobs, Asians: 26 to 40 percent. Asians
will continue to be represented well beyond their proportion in the general
population. Black and Hispanic PhDs in the selected areas are being turned
out at a slightly higher rate than we predict. However, the difference
is within the error of our calculation. We should expect that the future
will see Whites and Asians to continue to dominate this segment of the
job market, to the virtual exclusion of other groups. The close agreement
of doctorate production by race and ethnicity with the predicted proportions
of job holders suggests that the marketplace, at least for now, has reached
a steady state essentially free of external influences.